Various digital communication standards have adopted a convolutional coding method for a forward error correction (FCE).
An information bit sequence encoded in the convolutional coding method is decoded by a Viterbi decoder in a receiver.
FIG. 1 shows a diagram of a configuration of a convolutional encoder having a constraint length K of 7 according to the international standard IEEE 802.16.
As shown in FIG. 1, the convolutional encoder having the constraint length K of 7 according the international standard IEEE 802.16 includes two XOR operators 11 and 12 and six delay units 21 to 26. The convolutional encoder receives one bit among the information bit sequence for every clock signal through a first delay unit 21, and generates two encoded symbols by the two XOR operators 11 and 12. The convolutional code is classified as a zero-tail convolutional code and a tail-biting convolutional code.
The zero-tail convolutional encoding method will now be described with reference to FIG. 2 to FIG. 4.
FIG. 2 shows a diagram for representing an encoding unit packet of an encoder in the zero-tail convolutional encoding method.
As shown in FIG. 2, the encoding unit packet of the encoder in the zero-tail convolutional encoding method is formed by adding a sequence of (K−1) zero-bits (a zero-tail sequence) to the information bit sequence. Therefore, when the number of the information bits is L, the number of bits of the encoding unit packet of the encoder in the zero-tail convolutional encoding method is L+K−1. Since the constraint length K is 7 in an exemplary embodiment of the present invention, the encoding unit packet includes L+6 bits.
FIG. 3 shows a diagram for representing an initial state of the encoder in the zero-tail convolutional encoding method. As shown in FIG. 3, each delay unit has a value of 0 when the encoder in the zero-tail convolutional encoding method is at the initial state. Therefore, a Viterbi decoder in the zero-tail convolutional encoding method may start a decoding operation from the 0 state.
FIG. 4 shows a diagram for representing an ending state of the encoder in the zero-tail convolutional encoding method. As shown in FIG. 4, the ending state of the encoder in the zero-tail convolutional encoding method is the 0 state in which each delay unit has the value of 0. Since 0 values of the last K−1 bits of the encoding unit packet are inputted to the convolutional encoder, the ending state of the encoder in the zero-tail convolutional encoding method is becomes the 0 state. Therefore, the Viterbi decoder in the zero-tail convolutional encoding method may start a trace back operation from the 0 state.
Since the additional zero tail sequence having the values of 0 is used in the zero-tail convolutional encoding method, an error may be easily corrected when a last part of the information bit sequence has the error. In addition, the Viterbi decoder may start the decoding and trace back operations from the 0 state since both the initial and ending states of the convolutional encoder are 0, and therefore a configuration of the Viterbi decoder may be simplified. However, there is a problem in that the data rate is reduced due to the additional zero tail sequence in the zero-tail convolutional encoding method. To solve the problem, the tail biting convolutional encoding method has been suggested.
The tail biting convolutional encoding method will now be described with reference to FIG. 5 to FIG. 7.
FIG. 5 shows a diagram for representing an encoding unit packet of an encoder in the tail biting convolutional encoding method. As shown in FIG. 5, the encoding unit packet of the encoder in the tail biting convolutional encoding method has no additional data. Therefore, the data rate in the tail biting convolutional encoding method is better than that in the zero-tail convolutional encoding method.
FIG. 6 shows a diagram for representing an initial state of the encoder in the tail biting convolutional encoding method. As shown in FIG. 6, the initial state of the encoder in the tail biting convolutional encoding method is determined by the last 6 bits of the encoding unit packet. Since the last 6 bits of the encoding unit packet of the encoder in the tail biting convolutional encoding method are respectively not 0, the initial state of the encoder in the tail biting convolutional encoding method is not 0. The encoder in the tail biting convolutional encoding method preferentially receives the last 6 bits of the encoding unit packet before performing an encoding operation, so as to establish the initial state of the encoder as the last 6 bits of the decoding unit packet. At this time, the encoder in the tail biting convolutional encoding method does not generate an encoded output bit. Then, the encoder in the tail biting convolutional encoding method sequentially receives the information bit sequence, and generates the encoded output bit.
FIG. 7 shows a diagram for representing the ending state of the encoder in the tail biting convolutional encoding method. As shown in FIG. 7, differing from the zero-tail convolutional encoding method, the ending state in the tail biting convolutional encoding method is determined by the last 6 bits of the information bit sequence since the ending state includes no additional zero-bit. Therefore, the initial and ending states of the encoder in the tail biting convolutional encoding method are the same.
In addition, the initial and ending states of the encoder in the tail biting convolutional encoding method are not 0 since those are determined by the last 6 bits of the encoding unit packet. Therefore, the Viterbi decoder in the tail biting convolutional encoding method has a problem of determining the initial state for the decoding and trace back back operations, and therefore the configuration of the Viterbi decoder is problematically complicated. In addition, the initial state for the trace back operation may be falsely determined and the final decoded information bit sequence may include an error when the last part of the encoding unit packet has errors.
The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.